In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of modulus which itself means "a small measure") is often used to assert that two distinct mathematical objects can be regarded as equivalent—if their difference is accounted for by an additional factor.
It was initially introduced into mathematics in the context of modular arithmetic by Carl Friedrich Gauss in 1801.
[3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n. It is the Latin ablative of modulus, which itself means "a small measure.
Gauss originally intended to use "modulo" as follows: given the integers a, b and n, the expression a ≡ b (mod n) (pronounced "a is congruent to b modulo n") means that a − b is an integer multiple of n, or equivalently, a and b both leave the same remainder when divided by n. For example: means that In computing and computer science, the term can be used in several ways: The term "modulo" can be used differently—when referring to different mathematical structures.
For example: In general, modding out is a somewhat informal term that means declaring things equivalent that otherwise would be considered distinct.